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All Journal Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Mohd. Ariff Bin Admon
Universiti Teknologi Malaysia
Mathematics

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THE EXISTENCE AND UNIQUENESS OF THE MILD SOLUTION TO A NONLINEAR CAUCHY PROBLEM ASSOCIATED WITH A NONLOCAL REACTION-DIFFUSION SYSTEM Bambang Hendriya Guswanto; Mohd. Ariff Bin Admon; Nur Natasha Binti Lim Boon Chye
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 11 No 2 (2019): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2019.11.2.2264

Abstract

We study the existence and uniqueness of a mild solution to a nonlinear Cauchy problem associated with a nonlocal reaction diffusion system by employing the properties of analytic semigroup operator generated by the linear part of the problem which is sectorial and then applying Banach Fixed Point Theorem to the problem. We show that the problem has a unique mild solution under a Lipschitz condition on the nonlinear part of the problem. An example as an application of the result obtained is also given.
THE EXISTENCE AND UNIQUENESS OF THE MILD SOLUTION TO A NONLINEAR CAUCHY PROBLEM ASSOCIATED WITH A NONLOCAL REACTION-DIFFUSION SYSTEM Bambang Hendriya Guswanto; Mohd. Ariff Bin Admon; Nur Natasha Binti Lim Boon Chye
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Vol 11 No 2 (2019): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2019.11.2.2264

Abstract

We study the existence and uniqueness of a mild solution to a nonlinear Cauchy problem associated with a nonlocal reaction diffusion system by employing the properties of analytic semigroup operator generated by the linear part of the problem which is sectorial and then applying Banach Fixed Point Theorem to the problem. We show that the problem has a unique mild solution under a Lipschitz condition on the nonlinear part of the problem. An example as an application of the result obtained is also given.
Co-Authors Guswanto, Bambang Hendriya Nur Natasha Binti Lim Boon Chye